Motivation:

Pros:

I really liked the idea of the caveman grug and presenting how it’s important for him to know where to hunt and what to bring, and the visuals with that were great, and strongly supported the motivation, and the real-world examples for every section such as the wine barrels, paper aeroplane, walking up a hill, etc.

Cons:

That being said, I think for some people, having too many examples and jumping from one to the next too quickly can be difficult to follow, but personally I’d prefer too many examples than too few. All the examples were simple and clear though, so I didn’t think this was a big issue.

Clarity:

Pros:

Giving 5 levels was very useful in terms of presenting what’s going to be covered, and generally makes it easier to see what the video is about. The section on Linear Optimisation I found to be especially insightful, as doing D1 myself in further maths, I can say that this presented the topic very clearly. I also liked how you explained the idea of a derivative and gradient before moving on into the more complex topics.

Cons:

Whilst the section on introducing the derivative was useful, I feel like you glossed over how you move from linear functions to non-linear functions, and how you find their gradient. now admittedly, almost anyone who watches a video like this will know what a derivative is, but I feel there was an opportunity to introduce the formal definition of a derivative with $\lim_{h\rightarrow0}\ \frac{f(x+h) - f(x)}{h}$ In the third section with the part where you go through how Kepler related length, height, and radius, I thought that the animations played a little fast and that I needed a bit more time to go through the working,

Novelty:

Pros:

The topic of optimisation is used very often in maths explainers, but the variety you included with a broader view of the subject is something I appreciated, as I feel like linear programming is often not touched. I have background knowledge in sections 1-4, but section 5 with lagrangian optimisation isn’t something I’ve seen before, and I found it very interesting how you create a lagrangian function that you maximise in order to obtain the maximum value of a function with constraints. given that I haven’t seen this before, I’d say you did a excellent job of explaining it.

Cons:

A lot of people have done a similar thing to you, with having animations made with manim and talking over it in terms of the presenting, and in the earlier sections, I think there could’ve been a little more detail and explanation, but the earlier content is obviously explored much more than the later content in maths explainers, so naturally I’ll have higher expectations for that.

Memorability:

Pros:

As I said earlier, the visual explanations were very clear, and simply having them will make the video more memorable. Using real world examples and generally being very intuitive is something that’ll really make me remember this video well in weeks if not months to come.

Cons:

I don’t think there was really a distinctive “aha” moment that I could point out where everything seemed to line up, but I don’t think a video necessarily needs this to be good. It’s a nice addition, sure, but not vital.

Extra thoughts:

Pros:

The animations - especially at the start - were excellent throughout the video, everything was explained in a clear visual manner, but there a few improvements I would suggest (which I’ll put in the cons section) The audio quality was great, and everything was clear and well phrased, which quite a number of entries lack. I don’t know whether this would be a positive or negative, but I found that the quality of the video got better and better the longer I watched it. Whether this was because the topics got more complex and needed me to focus more, or whether it was just a case of the content, I found levels 3, 4, and 5 especially interesting, with 3 being my personal favourite.

Cons:

There’s quite a few stutters and slip ups in the video, and I did notice that you were using a script, but this a small part of the whole video and I really don’t expect you to learn scripts by heart, so this is just a small criticism. In terms of the animations, there are a few sections where you manipulate expressions and such where I think it’d be worth slowing down a bit, and one piece of advise I’d give is to keep your notation consistent. if you use $\bigg(\frac{h}{2}\bigg)^2$ in one line then $(h/2)^2$ in the next, I feel like that can throw people off a little, but again this is all a small part of the video, and content is king as grant would say.

Final Thoughts:

I thought this video was above the average maths explainer I’d see normally. For a first video on Youtube like this, I think you’ve given it a really good go, and whilst there’s always room for improvement, I think that this is a great video which would be good for other people to watch, and was certainly good for me. (Don’t treat my score as being the standard x/10, as 5 means about the same as every other video and 7 means better than most, and the standard of maths explainers is incredibly high nowadays, so please don’t be too disatisfied) Thanks!

Thanks for making this video! It’s unclear to me who this video is for. It feels like you wanted to walk through these optimisation techniques and so you tried to find examples that fit them. But your premise at the beginning is something like “humans need optimisation to solve useful problems”. If that’s what you want to show, then starting with cool problems, then applying optimisation principles to solve them is a good starting place. Whereas if you just want to walk through 5 optimisation techniques, then I’d think that’s what class is good for. I also want to say that the “5 levels of optimisation” is rather misleading since one technique is not necessarily better than the other. In many scenarios, a quadratic approximation is sufficient, or a first order approximation is good enough. I also think framing math concepts in terms of “5 levels of complexity” gives a bit of an elitist tinge because there are levels, but this is really just 5 cool optimisation techniques. On the flip side, great editing. The 3D animations are super entertaining and your camera/mic set up is super high quality.

Many nice animations and examples, but given the number of different topics, the amount of technical detail with each equation was hard to follow. Either this being a series of separate lessons and videos, or taking a higher up perspective comparing the geometric interpretation of each of these methods would have been easier to follow. As it was, we went into a lot of symbol manipulation solution detail through methods and notation that kept changing, making those low level details pretty hard to follow.

Specific details: Level 1 fitting a quadratic example - how do we fit a quadratic to data? It seems like implicitly by doing that we are deciding where to put the vertex thus already finding the maximum or minimum value wine barrel example - nice historical problem I hadn’t heard of, showing a derivative example that’s not just a quadratic. The solution was a lot of symbol manipulation with specific numbers, would have preferred to take away some general geometric understanding about the role of the diagonal line Level 4 - hard to follow with so much notation and symbols introduced. Much better would have been to try to represent what these are graphically. Especially true when showing the table and saying that things shown are not the general case. I was wondering if there was a visual interpretation for what H was actually calculating. Start of level 5 - constraints had already been mentioned in linear programming (tie back to level 2) Level 5 example - if we are just going along a line, wouldn’t we just substitute y as a function of x and then solve a single variable problem? Egg force example - again just a lot of numbers, once we derived the equation that looked like a constraint form wanted to see the graph of the constraint and objective

8:13 your skip timestamp is wrong, I assume it should be 9:11. If your video contains stuff that is bound to change in editing, maintain a todo-list to go through before final release and find a way to remind yourself of checking it. And don’t ever skip that procedure even for “quick fixes”.

Audio is quite desynced sometimes, for example at 10:30

Overall thoughts:

This is an impressive amount of work for a video created by recent high-school graduates, and especially for such an advanced topic. Some of the explanations in the later parts of the video were hard to follow.

Motivation:

The subject of optimisation is very nicely motivated.

Clarity:

The motivation of the video was clearly explained, and visuals such as the moving tangent line along a curve to illustrate maxima and minima coinciding with zero derivative were nice and aided clarity. In Level 1, I didn’t understand what the relevance of the mention of the local minima and local maxima was meant to be. Later on, the explanation of partial derivatives was quite fast. I struggled to follow what was going on in Level 5. Terms such as the “constraint function” were introduced very fast, and then were subsequently treated as if the viewer had a clear grasp of their meaning. Naturally, I then also had difficulty following the worked example at the end.

Novelty:

Examples such as the varied hunting optimisation problems for Grug, and the historical example of Kepler, were very creative ways to help us engage with the problem and show its breadth of importance.

Memorability:

There were very nicely presented ideas early on, but a viewer attempting to follow the 15 minutes of fast-paced technicalities dominating the second half of the video might end up having a more fuzzy memory of the nice aspects of the video.

This is a really well produced video but maybe tackles too many concepts in one. It might hold the audience better by splitting each level up into it’s own separate video.

Very nice visual transitions and 3D animation with Grug at the beginning. It looks like you already have experience with making videos since it looks more polished than what I would expect from a beginner. I checked your channel and it seems like you created your channel on Sep 1, the last day of the deadline. Cutting it close but you made it!

On to the video itself, I think it’s a great survey of the basic optimization techniques but I felt the video was really long. I sat through the whole 37 minutes to give the review but if I got recommended it on my YouTube feed I don’t think I could’ve done that. After watching it I felt like I could summarize the key takeaways in just a few bullet points

• Linear optimization
  • Linear objective function, linear inequality constraints
• Single variable optimization
  • Use standard calculus: solve for derivative = 0
• Multi variable optimization
  • Use multivariate calculus, with the some caveats on saddle points
• Constrained optimization
  • Use Lagrange multipliers
• etc.

I personally would’ve preferred to walk away with these key points in less time.

Really enjoyed this video, as a high school who is starting uni next year I found that that you made the harder multivariable optimization achievable to understand, by not getting stuck in the weeds of the math, which I found really helpful.
I also really appreciated the real world examples throughout which kept the video interesting. Although I am sad that Grog didn’t get more video time.

My only real critique would be that for people who haven’t encountered calculus the later part of the video (which was the most interesting) would have gone way over their heads. Because of this I felt like the explanations at the start (explaining differentiation) weren’t necessary as that wasn’t the audience that this was aimed at. Overall I thought this was minor as you gave people a timestamp to skip to and it didn’t take away from the overall video.

Great visuals and presentation along with choice of topic. The video is a bit lengthy but the motivations are made clear from the start in a relatable fashion and grows in complexity gradually.